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Existential Quantification of Counterfactuals.

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Wallows
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Existential Quantification of Counterfactuals.

Post by Wallows » December 15th, 2018, 1:14 pm

As requested I am reposting this topic to include some more content. This is not a homework assignment. Here it goes:

I have a question about predicate logic and modal logic.

Namely, do any of them overlap with one another? To give an example, does existential quantification apply to counterfactual statements?

A counterfactual statement can be something like "A possible world where I won the lottery." I wouldn't be able to assign an existential quantifier in the same manner that I could to a statement in this world, because that statement simply does not obtain or isn't instantiated in this world contrary to a possible world where I did indeed win the lottery.

Thank you.

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Wallows
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Re: Existential Quantification of Counterfactuals.

Post by Wallows » December 15th, 2018, 5:17 pm

This is relevant. Quine was opposed to quantification of modal relations.

https://plato.stanford.edu/entries/logi ... #QuaModLog

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ktz
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Re: Existential Quantification of Counterfactuals.

Post by ktz » December 15th, 2018, 9:25 pm

I'm not an expert on counterfactual theories of causation and I haven't taken any formal courses on modal logic. But I've taken discrete math and have a layman's interest in formal logic in general, so it's possible I can help. But can I ask you some question first?

Can I ask what your background is? Are you sure you have the prerequisite knowledge for this question? Like, if I sent you to the free online textbook, "Logic In Action", say, section 4.3, would the material on propositional logic be familiar to you or something you would be learning for the first time?

If you have experience with using existential quantifiers in propositional logic, could you clarify exactly for us what it is you are trying to do with the knowledge of the application of existential quantifiers to counterfactuals? Are you trying to understand the SEP section you linked? Are you trying to learn about counterfactual theories of causation? Are you trying to read Quine or Lewis just for fun?

The reason I am asking is because your phrasing doesn't sound to me like someone who has the prerequisite knowledge to the answer you are looking for. For example, your definition of counterfactuals is missing the fact that a counterfactual statement is a type of conditional. Conditionals are statements of the form, if some condition is true, then some expression is implied. The example you gave:
"A possible world where I won the lottery."
is not a conditional, so it is not a counterfactual, at least not the way they are referred to by Lewis, or in the context of counterfactual theories of causation. A counterfactual must be a conditional with an antecedent that is assumed false, so something like:
If someone had played the winning numbers, then that person would have won the lottery.
A counterfactual is not just something counter to the facts. In the example I gave, it's possible that someone could have played the winning numbers for the lottery and I just didn't know before making the statement. So counterfactuals can have true antecedents and exist in our world. The reason they are called counterfactuals is they implicitly assume the antecedent to be counter to the facts -- even though that assumption could be incorrect, and counterfactuals could describe a real situation like if someone actually did play the winning numbers and won the lottery but didn't tell me.
Wallows wrote:
December 15th, 2018, 5:17 pm
This is relevant. Quine was opposed to quantification of modal relations.

https://plato.stanford.edu/entries/logi ... #QuaModLog
Counterfactuals are not exclusive to modal logic, so it's debatable whether Quine's criticisms are all that relevant to your original question the way you composed it. Are these criticisms the crux of what you are trying to understand? If so, you should ask that directly, instead of using the terminology incorrectly.

If it's Quine's criticisms of modal logic you want to understand, would you be able to find the answer for yourself if I sent you to this introduction to modal logic, and then this series of videos discussing those criticisms directly?
You may have a heart of gold, but so does a hard-boiled egg.

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ktz
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Re: Existential Quantification of Counterfactuals.

Post by ktz » December 15th, 2018, 9:27 pm

Sorry, gave the wrong link for the modal logic introduction:

http://rkirsling.github.io/modallogic/
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Wallows
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Re: Existential Quantification of Counterfactuals.

Post by Wallows » December 15th, 2018, 9:46 pm

ktz wrote:
December 15th, 2018, 9:25 pm
If you have experience with using existential quantifiers in propositional logic, could you clarify exactly for us what it is you are trying to do with the knowledge of the application of existential quantifiers to counterfactuals? Are you trying to understand the SEP section you linked? Are you trying to learn about counterfactual theories of causation? Are you trying to read Quine or Lewis just for fun?
Well, philosophy has been my hobby for about 15 years now, and I'm reading Kripke's Naming and Necessity. I'm also trying to understand the SEP entry mentioned above.
The reason I am asking is because your phrasing doesn't sound to me like someone who has the prerequisite knowledge to the answer you are looking for. For example, your definition of counterfactuals is missing the fact that a counterfactual statement is a type of conditional. Conditionals are statements of the form, if some condition is true, then some expression is implied. The example you gave:
"A possible world where I won the lottery."
is not a conditional, so it is not a counterfactual, at least not the way they are referred to by Lewis, or in the context of counterfactual theories of causation. A counterfactual must be a conditional with an antecedent that is assumed false, so something like:
If someone had played the winning numbers, then that person would have won the lottery.
I understand, and sorry for the blunder. I have studied some formal logic; but, does my wording fundamentally change the import of my question. Perhaps, it's a priori that a counterfactual is indeed a condition upon which our world depends on assessing.
A counterfactual is not just something counter to the facts. In the example I gave, it's possible that someone could have played the winning numbers for the lottery and I just didn't know before making the statement. So counterfactuals can have true antecedents and exist in our world. The reason they are called counterfactuals is they implicitly assume the antecedent to be counter to the facts -- even though that assumption could be incorrect, and counterfactuals could describe a real situation like if someone actually did play the winning numbers and won the lottery but didn't tell me.
So, basically if I say that something could have occured otherwise based on a fact, then I am entertaining the idea that fact's could have happened otherwise; but, strictly speaking with respect to our own world, yes?

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Wallows
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Re: Existential Quantification of Counterfactuals.

Post by Wallows » December 16th, 2018, 4:30 pm

(I removed the links that were preventing this post from being posted)

We can only "measure" (quantify) counterfactuals by an accessibility relation to our own world (stipulation or instantiation). Therefore how can we assert something as necessarily true in all possible world's if quantification of modal relations (counterfactuals) is/are restricted to only our world?

I'm also interested if frame conditions have anything to do with this?.

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Re: Existential Quantification of Counterfactuals.

Post by Mosesquine » December 23rd, 2018, 7:02 am

Today's most popular-almost-standard theory of counterfactual conditionals is so-called Lewis-Stalnaker theory. It, Lewis-Stalnaker theory, says that counterfactuals are conditionals when their antecedents are true, then their consequents are also true in the worlds in which the former ones are true. Consider, for example, the following statement:

If it were the case that the Prime Minister of Alpha Centauri had no money, then it would be the case that the Prime Minister of Alpha Centauri could not buy some snacks.

This conditional means that all possibilities that the antecedent is the case (i.e. "the Prime Minister of Alpha Centauri had no money") make the consequent (i.e. "the Prime Minister of Alpha Centauri could not by some snacks") be true. Some counter-examples of counterfactual relations might be good objections, of course (such as "some patrons of the Prime Minister helped", and so on).

The following list is a set of good sources to learn the formal aspects of counterfactuals:

David Lewis, Counterfactuals.
Ted Sider, Logic for Philosophy.
Scott Soames, Philosophy of Language.

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